TOMS462
Bivariate Normal Distribution

TOMS462 is a MATLAB library which evaluates the upper right tail of the bivariate normal distribution; that is, the probability that normal variables X and Y with correlation R will satisfy H <= X and K <= Y.

While the text of many ACM TOMS algorithms is available online through ACM: http://www.acm.org/pubs/calgo or NETLIB: http://www.netlib.org/toms/index.html, most of the early algorithms are not available. This is one of them. I typed it in.

Usage:

value = bivnor ( ah, ak, r )

computes VALUE, the probability that two variables, X and Y related by a bivariate normal distribution with correlation R, satisfy AH <= X and AK <= Y.

Languages:

TOMS462 is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

OWENS, a MATLAB library which evaluates Owen's T function.

PROB, a MATLAB library which contains a number of routines for evaluating cumulative distribution functions.

TEST_VALUES, a MATLAB library which supplies test values of various mathematical functions.

Reference:

1. Thomas Donnelly,
   Algorithm 462: Bivariate Normal Distribution,
   Communications of the ACM,
   October 1973, Volume 16, Number 10, page 638.
2. Donald Owen,
   Tables for Computing Bivariate Normal Probabilities,
   Annals of Mathematical Statistics,
   Volume 27, Number 4, pages 1075-1090, December 1956.

Source Code:

• bivnor.m computes the bivariate CDF.
• bivariate_normal_cdf_values.m, returns some values of the bivariate normal CDF.
• timestamp.m, returns the YMDHMS date as a timestamp.

Examples and Tests:

• toms462_test.m, calls all the tests.
• toms462_test_output.txt, the output file.
• toms462_test01.m, makes a quick check against data accurate to three digits.
• toms462_test02.m, compares the computation to a set of tabulated data.

You can go up one level to the MATLAB source codes.